Something well-thought-out has been planned carefully and thoroughly, with the difficulties worked through in advance. You use it about plans, designs, arguments, essays, laws, apps, lessons, rooms — anything a person had to think their way through before making.

What the word really praises is the thinking you cannot see. A well-thought-out design is one where, when you try to break it, someone has already been there: the awkward case is handled, the objection is answered, the drawer opens without hitting the door. Its opposite tells you as much as the word itself. When something is called 'not very well thought out', the complaint is never that the idea was stupid — it is that nobody sat with it long enough to notice the obvious problem.

It is measured, slightly formal praise, at home in reviews, reports, feedback on student work, and meetings. It is also cool rather than warm: calling a proposal well-thought-out says it is solid and sensible, but it stops short of calling it exciting. If you wanted to say the idea was brilliant, you would say that instead.

About the hyphens, since they look alarming. Before a noun, hyphenate the whole thing: a well-thought-out plan. After the verb, drop them all: the plan was well thought out. You will see other people's versions vary, and nobody will mind much, but that is the tidy rule.